In a driving system of a single phase induction motor of the related art, a single phase power supply is directly connected to an induction motor. FIG. 1a shows the driving system of the single phase induction motor (a squirrel cage type induction motor) of the related art, which is called a direct input moving driving system. FIG. 1b and FIG. 1c shows graphs illustrating a relationship of a velocity-torque curve and a velocity-rotor current at the direct input driving time of the single phase induction motor of the related art. The vertical axis of FIG. 1b represents the output maximum torque, and the horizontal axis represents a value obtained by normalizing an electrical angle rotation velocity of a rotor by a frequency of a system voltage (Wn=Wr/We). A high output torque is represented only in the vicinity of the frequency of a system voltage (Wn=+1, −1), and it is difficult to vary the torque at a constant velocity. Above everything else, there is no torque at a velocity of 0, and thus it is difficult to perform initial moving. That is, when the velocity of the inductor motor is 0, that is, in a situation where the inductor motor is stopped, it does not have any torque value. For this reason, there is a problem that it is difficult to perform the initial moving of the induction motor. In other words, for the initial moving of the induction motor, a separate moving circuit or a mechanical device disclosed in Korean Laid-Open Patent Publication No. 10-2005-0085204 is necessary. As a result, an induction motor driving system is complex, and a configuration thereof is inefficient. Referring to FIG. 1c, at a velocity in the vicinity of the frequency of a system voltage, that is, except for a low slip section, it can be confirmed that a rotor current deviates from a rated current. That is, a driving area is very restricted. When deviating from the rated current, it is also difficult to control the velocity of the motor. In the direct input moving driving system control, the moving velocity is only determined according to the magnitude of load, and a power factor of a single phase grid is not also secured.